Maximally accreting supermassive stars: a fundamental limit imposed by hydrostatic equilibrium

Context. Major mergers of gas-rich galaxies provide promising conditions for the formation of supermassive black holes (SMBHs; ≳10⁵ M_⊙) by direct collapse because they can trigger mass inflows as high as 10⁴ - 10⁵ M_⊙ yr^-1 on sub-parsec scales. However, the channel of SMBH formation in this case, either dark collapse (direct collapse without prior stellar phase) or supermassive star (SMS; ≳10⁴ M_⊙), remains unknown.
Aims: Here, we investigate the limit in accretion rate up to which stars can maintain hydrostatic equilibrium.
Methods: We compute hydrostatic models of SMSs accreting at 1-1000 M_⊙ yr^-1, and estimate the departures from equilibrium a posteriori by taking into account the finite speed of sound.
Results: We find that stars accreting above the atomic cooling limit (≳10 M_⊙ yr^-1) can only maintain hydrostatic equilibrium once they are supermassive. In this case, they evolve adiabatically with a hylotropic structure, that is, entropy is locally conserved and scales with the square root of the mass coordinate.
Conclusions: Our results imply that stars can only become supermassive by accretion at the rates of atomically cooled haloes (∼0.1 - 10 M_⊙ yr^-1). Once they are supermassive, larger rates are possible.